{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T03:55:43Z","timestamp":1785902143282,"version":"3.56.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,12,19]],"date-time":"2018-12-19T00:00:00Z","timestamp":1545177600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Finance Stoch"],"published-print":{"date-parts":[[2019,1]]},"DOI":"10.1007\/s00780-018-00381-0","type":"journal-article","created":{"date-parts":[[2018,12,19]],"date-time":"2018-12-19T05:44:45Z","timestamp":1545198285000},"page":"173-207","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["A paradox in time-consistency in the mean\u2013variance problem?"],"prefix":"10.1007","volume":"23","author":[{"given":"Alain","family":"Bensoussan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kwok Chuen","family":"Wong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sheung Chi Phillip","family":"Yam","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2018,12,19]]},"reference":[{"key":"381_CR1","doi-asserted-by":"publisher","first-page":"2970","DOI":"10.1093\/rfs\/hhq028","volume":"23","author":"S. Basak","year":"2010","unstructured":"Basak, S., Chabakauri, G.: Dynamic mean\u2013variance asset allocation. Rev. Financ. Stud. 23, 2970\u20133016 (2010)","journal-title":"Rev. Financ. Stud."},{"key":"381_CR2","volume-title":"Dynamic Programming","author":"R.E. Bellman","year":"1957","unstructured":"Bellman, R.E.: Dynamic Programming. Princeton University Press, Princeton (1957)"},{"key":"381_CR3","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1137\/130914139","volume":"5","author":"A. Bensoussan","year":"2014","unstructured":"Bensoussan, A., Wong, K.C., Yam, S.C.P., Yung, S.P.: Time-consistent portfolio selection under short-selling prohibition: from discrete to continuous setting. SIAM J. Financ. Math. 5, 153\u2013190 (2014)","journal-title":"SIAM J. Financ. Math."},{"key":"381_CR4","unstructured":"Bj\u00f6rk, T., Khapko, M., Murgoci, A.: Time inconsistent stochastic control in continuous time: theory and examples. Working Paper (2016). Available online at \n                    arXiv:1612.03650"},{"key":"381_CR5","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1007\/s00780-014-0234-y","volume":"18","author":"T. Bj\u00f6rk","year":"2014","unstructured":"Bj\u00f6rk, T., Murgoci, A.: A theory of Markovian time inconsistent stochastic control in discrete time. Finance Stoch. 18, 545\u2013592 (2014)","journal-title":"Finance Stoch."},{"key":"381_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.1467-9965.2011.00515.x","volume":"24","author":"T. Bj\u00f6rk","year":"2014","unstructured":"Bj\u00f6rk, T., Murgoci, A., Zhou, X.Y.: Mean\u2013variance portfolio optimization with state-dependent risk aversion. Math. Finance 24, 1\u201324 (2014)","journal-title":"Math. Finance"},{"key":"381_CR7","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.jedc.2016.12.001","volume":"75","author":"X.Y. Cui","year":"2017","unstructured":"Cui, X.Y., Li, D., Shi, Y.: Self-coordination in time inconsistent stochastic decision problems: a\u00a0planner-doer game framework. J. Econ. Dyn. Control 75, 91\u2013113 (2017)","journal-title":"J. Econ. Dyn. Control"},{"key":"381_CR8","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/s00780-012-0189-9","volume":"17","author":"C. Czichowsky","year":"2013","unstructured":"Czichowsky, C.: Time-consistent mean\u2013variance portfolio selection in discrete and continuous time. Finance Stoch. 17, 227\u2013271 (2013)","journal-title":"Finance Stoch."},{"key":"381_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/100810034","volume":"3","author":"I. Ekeland","year":"2012","unstructured":"Ekeland, I., Mbodj, O., Pirvu, T.A.: Time-consistent portfolio management. SIAM J. Financ. Math. 3, 1\u201332 (2012)","journal-title":"SIAM J. Financ. Math."},{"key":"381_CR10","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s11579-008-0014-6","volume":"2","author":"I. Ekeland","year":"2008","unstructured":"Ekeland, I., Pirvu, T.A.: Investment and consumption without commitment. Math. Financ. Econ. 2, 57\u201386 (2008)","journal-title":"Math. Financ. Econ."},{"key":"381_CR11","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1016\/j.ejor.2010.09.038","volume":"209","author":"P.A. Forsyth","year":"2011","unstructured":"Forsyth, P.A., Wang, J.: Continuous time mean variance asset allocation: a time-consistent strategy. Eur. J. Oper. Res. 209, 184\u2013201 (2011)","journal-title":"Eur. J. Oper. Res."},{"key":"381_CR12","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1093\/qje\/qjs051","volume":"128","author":"C. Harris","year":"2013","unstructured":"Harris, C., Laibson, D.: Instantaneous gratification. Q. J. Econ. 128, 205\u2013248 (2013)","journal-title":"Q. J. Econ."},{"key":"381_CR13","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1016\/j.jet.2005.07.006","volume":"132","author":"L.S. Karp","year":"2007","unstructured":"Karp, L.S.: Non-constant discounting in continuous time. J. Econ. Theory 132, 557\u2013568 (2007)","journal-title":"J. Econ. Theory"},{"key":"381_CR14","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/s00245-014-9267-z","volume":"71","author":"M.T. Kronborg","year":"2015","unstructured":"Kronborg, M.T., Steffensen, M.: Inconsistent investment and consumption problems. Appl. Math. Optim. 71, 473\u2013515 (2015)","journal-title":"Appl. Math. Optim."},{"key":"381_CR15","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/s002450010003","volume":"42","author":"D. Li","year":"2000","unstructured":"Li, D., Zhou, X.Y.: Continuous-time mean\u2013variance portfolio selection: a stochastic LQ framework. Appl. Math. Optim. 42, 19\u201333 (2000)","journal-title":"Appl. Math. Optim."},{"key":"381_CR16","doi-asserted-by":"publisher","first-page":"860","DOI":"10.1016\/j.ejor.2009.04.005","volume":"201","author":"J. Mar\u00edn-Solano","year":"2010","unstructured":"Mar\u00edn-Solano, J., Navas, J.: Consumption and portfolio rules for time-inconsistent investors. Eur. J. Oper. Res. 201, 860\u2013872 (2010)","journal-title":"Eur. J. Oper. Res."},{"key":"381_CR17","first-page":"77","volume":"7","author":"H. Markowitz","year":"1952","unstructured":"Markowitz, H.: Portfolio selection. J. Finance 7, 77\u201391 (1952)","journal-title":"J. Finance"},{"key":"381_CR18","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s11579-016-0174-8","volume":"11","author":"J.L. Pedersen","year":"2017","unstructured":"Pedersen, J.L., Peskir, G.: Optimal mean\u2013variance portfolio selection. Math. Financ. Econ. 11, 137\u2013160 (2017)","journal-title":"Math. Financ. Econ."},{"key":"381_CR19","doi-asserted-by":"publisher","first-page":"185","DOI":"10.2307\/2296547","volume":"35","author":"E.S. Phelps","year":"1968","unstructured":"Phelps, E.S., Pollak, R.A.: On second-best national saving and game-equilibrium growth. Rev. Econ. Stud. 35, 185\u2013199 (1968)","journal-title":"Rev. Econ. Stud."},{"key":"381_CR20","doi-asserted-by":"publisher","first-page":"201","DOI":"10.2307\/2296548","volume":"35","author":"R.A. Pollak","year":"1968","unstructured":"Pollak, R.A.: Consistent planning. Rev. Econ. Stud. 35, 201\u2013208 (1968)","journal-title":"Rev. Econ. Stud."},{"key":"381_CR21","doi-asserted-by":"publisher","first-page":"391","DOI":"10.2307\/2296458","volume":"40","author":"B. Peleg","year":"1973","unstructured":"Peleg, B., Yaari, M.E.: On the existence of a consistent course of action when tastes are changing. Rev. Econ. Stud. 40, 391\u2013401 (1973)","journal-title":"Rev. Econ. Stud."},{"key":"381_CR22","first-page":"1177","volume-title":"Encyclopedia of Quantitative Finance","author":"M. Schweizer","year":"2010","unstructured":"Schweizer, M.: Mean\u2013variance hedging. In: Cont, R. (ed.) Encyclopedia of Quantitative Finance, pp.\u00a01177\u20131181. Wiley, New York (2010)"},{"key":"381_CR23","doi-asserted-by":"publisher","first-page":"165","DOI":"10.2307\/2295722","volume":"23","author":"R.H. Strotz","year":"1955","unstructured":"Strotz, R.H.: Myopia and inconsistency in dynamic utility maximization. Rev. Econ. Stud. 23, 165\u2013180 (1955)","journal-title":"Rev. Econ. Stud."},{"key":"381_CR24","unstructured":"Vigna, E.: Tail optimality and preferences consistency for intertemporal optimization problems. Working Paper, Collegio Carlo Alberto 502 (2017). Available online at \n                    https:\/\/www.carloalberto.org\/assets\/working-papers\/no.502.pdf"}],"container-title":["Finance and Stochastics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00780-018-00381-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00780-018-00381-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00780-018-00381-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,18]],"date-time":"2019-12-18T19:13:22Z","timestamp":1576696402000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00780-018-00381-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,19]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["381"],"URL":"https:\/\/doi.org\/10.1007\/s00780-018-00381-0","relation":{},"ISSN":["0949-2984","1432-1122"],"issn-type":[{"value":"0949-2984","type":"print"},{"value":"1432-1122","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,19]]},"assertion":[{"value":"7 October 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 September 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 December 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}